# Quality Diversity for Multi-task Optimization

arXiv: https://arxiv.org/abs/2003.04407 · HTML: https://mlsanity.com/paper/2003.04407/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 23 of 23)

- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [pyribs: A Bare-Bones Python Library for Quality Diversity Optimization](https://mlsanity.com/paper/2303.00191/) (2023)
- [Dynamics-Aware Quality-Diversity for Efficient Learning of Skill Repertoires](https://mlsanity.com/paper/2109.08522/) (2021)
- [Multi-Objective Quality Diversity Optimization](https://mlsanity.com/paper/2202.03057/) (2022)
- [B2Opt: Learning to Optimize Black-box Optimization with Little Budget](https://mlsanity.com/paper/2304.11787/) (2023)
- [Meta Learning Black-Box Population-Based Optimizers](https://mlsanity.com/paper/2103.03526/) (2021)
- [Half a Dozen Real-World Applications of Evolutionary Multitasking, and More](https://mlsanity.com/paper/2109.13101/) (2021)
- [Relevance-guided Unsupervised Discovery of Abilities with Quality-Diversity Algorithms](https://mlsanity.com/paper/2204.09828/) (2022)
- [Learning to Walk Autonomously via Reset-Free Quality-Diversity](https://mlsanity.com/paper/2204.03655/) (2022)
- [Online Damage Recovery for Physical Robots with Hierarchical Quality-Diversity](https://mlsanity.com/paper/2210.09918/) (2022)
- [Hierarchical Quality-Diversity for Online Damage Recovery](https://mlsanity.com/paper/2204.05726/) (2022)
- [Parametric-Task MAP-Elites](https://mlsanity.com/paper/2402.01275/) (2024)
- [(θl, θu)-Parametric Multi-Task Optimization: Joint Search in Solution and Infinite Task Spaces](https://mlsanity.com/paper/2503.08394/) (2025)
- [Efficient Learning of Locomotion Skills through the Discovery of Diverse Environmental Trajectory Generator Priors](https://mlsanity.com/paper/2210.04819/) (2022)
- [Towards QD-suite: developing a set of benchmarks for Quality-Diversity algorithms](https://mlsanity.com/paper/2205.03207/) (2022)
- [Interactive LLM-assisted Curriculum Learning for Multi-Task Evolutionary Policy Search](https://mlsanity.com/paper/2602.10891/) (2026)
- [Beyond Single-Model Optimization: Preserving Plasticity in Continual Reinforcement Learning](https://mlsanity.com/paper/2604.15414/) (2026)
- [Quality-Diversity Optimization as Multi-Objective Optimization](https://mlsanity.com/paper/2602.00478/) (2026)
- [Multi-Task Optimization over Networks of Tasks](https://mlsanity.com/paper/2604.21991/) (2026)
- [MOSAIC: Adversarial Co-evolution of Specialist Heuristics and Problem Instances for LLM-based Automated Heuristic Design](https://mlsanity.com/paper/2608.07544/) (2026)
- [Contextual Quality-Diversity Evolutionary Reinforcement Learning for HVAC Control in Tropical Commercial Buildings](https://mlsanity.com/paper/2608.11324/) (2026)
- [Towards Efficient Evaluation of Evolutionary Transfer Optimization: Case Studies on Task-Parameterized Applications](https://mlsanity.com/paper/2609.05040/) (2026)
- [In-Context Guidance: Learning Inter-Task Synergies via Numerical Foundational Models for Few-Shot Multitask Optimization](https://mlsanity.com/paper/2609.25836/) (2026)

## Abstract (arXiv)

Quality Diversity (QD) algorithms are a recent family of optimization algorithms that search for a large set of diverse but high-performing solutions. In some specific situations, they can solve multiple tasks at once. For instance, they can find the joint positions required for a robotic arm to reach a set of points, which can also be solved by running a classic optimizer for each target point. However, they cannot solve multiple tasks when the fitness needs to be evaluated independently for each task (e.g., optimizing policies to grasp many different objects). In this paper, we propose an extension of the MAP-Elites algorithm, called Multi-task MAP-Elites, that solves multiple tasks when the fitness function depends on the task. We evaluate it on a simulated parameterized planar arm (10-dimensional search space; 5000 tasks) and on a simulated 6-legged robot with legs of different lengths (36-dimensional search space; 2000 tasks). The results show that in both cases our algorithm outperforms the optimization of each task separately with the CMA-ES algorithm.